Algebra Examples

$\frac{3 y - 6}{2 y} = \frac{17}{3}$

Step 1

Factor $3$ out of $3 y - 6$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $3 y$ .

$\frac{3 (y) - 6}{2 y} = \frac{17}{3}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{3 y + 3 \cdot - 2}{2 y} = \frac{17}{3}$

Step 1.3

Factor $3$ out of $3 y + 3 \cdot - 2$ .

$\frac{3 (y - 2)}{2 y} = \frac{17}{3}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$3 (y - 2) \cdot 3 = 2 y \cdot 17$

Step 3

Solve the equation for $y$ .

Tap for more steps...

Step 3.1

Simplify $3 (y - 2) \cdot 3$ .

Tap for more steps...

Step 3.1.1

Rewrite.

$0 + 0 + 3 (y - 2) \cdot 3 = 2 y \cdot 17$

Step 3.1.2

Simplify by adding zeros.

$3 (y - 2) \cdot 3 = 2 y \cdot 17$

Step 3.1.3

Apply the distributive property.

$(3 y + 3 \cdot - 2) \cdot 3 = 2 y \cdot 17$

Step 3.1.4

Multiply $3$ by $- 2$ .

$(3 y - 6) \cdot 3 = 2 y \cdot 17$

Step 3.1.5

Apply the distributive property.

$3 y \cdot 3 - 6 \cdot 3 = 2 y \cdot 17$

Step 3.1.6

Multiply.

Tap for more steps...

Step 3.1.6.1

Multiply $3$ by $3$ .

$9 y - 6 \cdot 3 = 2 y \cdot 17$

Step 3.1.6.2

Multiply $- 6$ by $3$ .

$9 y - 18 = 2 y \cdot 17$

Step 3.2

Multiply $17$ by $2$ .

$9 y - 18 = 34 y$

Step 3.3

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 3.3.1

Subtract $34 y$ from both sides of the equation.

$9 y - 18 - 34 y = 0$

Step 3.3.2

Subtract $34 y$ from $9 y$ .

$- 25 y - 18 = 0$

Step 3.4

Add $18$ to both sides of the equation.

$- 25 y = 18$

Step 3.5

Divide each term in $- 25 y = 18$ by $- 25$ and simplify.

Tap for more steps...

Step 3.5.1

Divide each term in $- 25 y = 18$ by $- 25$ .

$\frac{- 25 y}{- 25} = \frac{18}{- 25}$

Step 3.5.2

Simplify the left side.

Tap for more steps...

Step 3.5.2.1

Cancel the common factor of $- 25$ .

Tap for more steps...

Step 3.5.2.1.1

Cancel the common factor.

$\frac{- 25 y}{- 25} = \frac{18}{- 25}$

Step 3.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{- 25}$

Step 3.5.3

Simplify the right side.

Tap for more steps...

Step 3.5.3.1

Move the negative in front of the fraction.

$y = - \frac{18}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{18}{25}$

Decimal Form:

$y = - 0.72$